Cryptology ePrint Archive: Report 2012/708

Calling out Cheaters: Covert Security With Public Verifiability

Gilad Asharov and Claudio Orlandi

Abstract: We introduce the notion of covert security with public verifiability, building on the covert security model introduced by Aumann and Lindell (TCC 2007). Protocols that satisfy covert security guarantee that the honest parties involved in the protocol will notice any cheating attempt with some constant probability $\epsilon$. The idea behind the model is that the fear of being caught cheating will be enough of a deterrent to prevent any cheating attempt. However, in the basic covert security model, the honest parties are not able to persuade any third party (say, a judge) that a cheating occurred.

We propose (and formally define) an extension of the model where, when an honest party detects cheating, it also receives a certificate that can be published and used to persuade other parties, without revealing any information about the honest party's input. In addition, malicious parties cannot create fake certificates in the attempt of framing innocents.

Finally, we construct a secure two-party computation protocol for any functionality $f$ that satisfies our definition, and our protocol is almost as efficient as the one of Aumann and Lindell. We believe that the fear of a public humiliation or even legal consequences vastly exceeds the deterrent given by standard covert security. Therefore, even a small value of the deterrent factor $\epsilon$ will suffice in discouraging any cheating attempt.

As the overall complexity of covert security and the parameter $\epsilon$ are inversely proportional to each other, we believe that the small price to pay to get the public verifiability property on top of covert security will be dominated by the efficiency gain obtained by using a smaller value $\epsilon$.